Knight--Walras Equilibria

TL;DR

This paper introduces Knight--Walras equilibria under Knightian uncertainty, establishing their existence, analyzing their efficiency properties, and comparing them with classical Arrow--Debreu equilibria, highlighting issues of robustness and inefficiency.

Contribution

It develops a new equilibrium concept for markets with nonlinear expectations due to Knightian uncertainty and proves their existence, linking them to classical equilibria and efficiency concepts.

Findings

Knight--Walras equilibria exist under nonlinear expectations.

Such equilibria are generally inefficient unless net trades are ambiguity-free.

Arrow--Debreu equilibria are non-robust to Knightian uncertainty.

Abstract

Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and establish their existence. In general, such equilibria lead to Pareto inefficiency and coincide with Arrow--Debreu equilibria only if the values of net trades are ambiguity--free in the mean. Without aggregate uncertainty, inefficiencies arise generically. We introduce a constrained efficiency concept, uncertainty--neutral efficiency and show that Knight--Walras equilibrium allocations are efficient in this constrained sense. Arrow--Debreu equilibria turn out to be non--robust with respect to the introduction of Knightian uncertainty.